Moreover, there are also other analytic methods for improving the QCD perturbation theory [1]}.
These generally involve some criterion for making a choice of the renormalization scale \(\mu \) , or other parameters that characterize a renormalization scheme, so that the perturbative result best approximates the exact (scheme-independent) result.
In this context, we mention the “Optimized Perturbation Theory”, which consists in improving the convergence of the perturbative expansion by choosing the value of \(\mu \)  according to a criterion of minimum sensitivity [2]}, [3]}. We also point out the “Fastest Apparent Convergence” technique [4]}, [5]}, that amounts to selecting the scale \(\mu \)  so that the next-to leading and higher order coefficients of the perturbative series are set to zero. This optimization procedure is related to effective charges [4]}, [5]}, [8]}, [9]}, which
consist in defining new running couplings that are more directly connected with physical observables. In addition, we mention the “Principle of Maximum Conformality” [1]} which improves the QCD predictive power by removing the dependence of physical predictions on the choice of the renormalization scheme. There has also been much work towards unifying the different approaches,
including the AdS-CFT/Dyson-Schwinger methods [11]}, [12]},
which may lead to a consistent universal running coupling in QCD.
